Word of the Week Wednesday: Mathematical Invariance

Definition: In Einstein’s use of the word, mathematical invariance established a genuine ontology in which the subject grips with objective structures and intrinsic intelligibility of the universe.

More about the word: Throughout Einstein’s work, the mechanistic universe proved unsatisfactory. This was made evident after the discovery of the electromagnetic field and the failure of Newtonian physics to account for it in mechanistic concepts. Then came the discovery of four-dimensional geometry and with it the realization that the geometrical structures of Newtonian physics could not be detached from changes in space and time with which field theory operated. Einstein stepped back into stride with Newton and his cognitive instrument of free invention. It was free in the sense that conclusions were not reached under logical control from fixed premises, and it was invented under the pressure of the nature of the universe upon the intuitive apprehension of it. Einstein used Newton and Maxwell’s partial differential equations in field theory to develop a mode of rationality called mathematical invariance.